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Problem Formulations and Numerical Analysis in Interger Programming and Combinatorial Optimization
Stephen C. Graves,Jeremy F. Shapiro +1 more
- 01 Dec 1979
TL;DR: In this paper, the authors present a list of the most important words in the English language: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~, ~~~~~~~~~~~~~~~~~~~~~~, ~~~ ~~~~~~~~~~~~~.
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Abstract: -~ ~ ; , I I .1 ~~~~ . -. ~ ~ % ~~ ~ -, ~ ~ ~ ~~! ,~ ~ : ~~. ,.-., ~ ~~. , .I -; -1 ~ ~ ~ ~ , . -, -, _I . ,. . . . ? .,.. -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. .II ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~~~i,.~ ~ ~ ~ ~ ~ ~~~~~~~~i '~; " ' ,~:~-.~ ,i ~ -~II 4 ,-)~ ? ~~~~-.. I... ... Z,.-~--. ... .... ! ~ . ~,-,~ . ,. ~L, ~,~ I: ; r~~ .... .,. . ~ -.~:. ,. . .: I~~~ ~ ~ ~ . ....~t. I .. ~ , ,. . , ,~, ~ , . -,;.: , , . : ~~~~~~'"~i :.. . , ? , , ;.:: -~ ~~~ ~~~~~~~~~~~~~~~~~~~~~~~,.;.. ,. . .
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References
The Traveling-Salesman Problem and Minimum Spanning Trees
Michael Held,Richard M. Karp +1 more
TL;DR: It is shown that maxπwπ = C* precisely when a certain well-known linear program has an optimal solution in integers.
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Multicommodity Distribution System Design by Benders Decomposition
Arthur M. Geoffrion,G. W. Graves +1 more
TL;DR: In this paper, a multicommodity capacitated single-period version of the problem is formulated as a mixed integer linear program, and a solution technique based on Benders Decomposition is developed, implemented, and successfully applied to a real problem for a major food firm with 17 commodity classes, 14 plants, 45 possible distribution center sites, and 121 customer zones.
1.2K
The traveling-salesman problem and minimum spanning trees: Part II
Michael Held,Richard M. Karp +1 more
TL;DR: An efficient iterative method for approximating this bound closely from below is presented, and a branch-and-bound procedure based upon these considerations has easily produced proven optimum solutions to all traveling-salesman problems presented to it.
1.1K
The Time-Dependent Traveling Salesman Problem and Its Application to the Tardiness Problem in One-Machine Scheduling
TL;DR: The optimization method described here combines finding shortest paths in an associated multipartite network with subgradient optimization and some branch-and-bound enumeration and gives computational results for the weighted tardiness problem.
323
The Travelling Salesman Problem and Related Problems
Bezalel Gavish,Stephen C. Graves +1 more
- 01 Jul 1978
TL;DR: Research supported, in part, by the Office of Naval Research under Contract N00014-75-C-0556.
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